Quasisymmetric graphs and Zygmund functions

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Abstract

A quasisymmetric graph is a curve whose projection onto a line is a quasisymmetric map. We show that this class of curves is related to solutions of the reduced Beltrami equation and to a generalization of the Zygmund class Λ*. This relation makes it possible to use the tools of harmonic analysis to construct nontrivial examples of quasisymmetric graphs and of quasiconformal maps. Kovalev was supported by the NSF grant DMS-0968756.

Original languageEnglish (US)
Pages (from-to)343-361
Number of pages19
JournalJournal d'Analyse Mathematique
Volume118
Issue number1
DOIs
StatePublished - Oct 2012

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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